Employment law and attitudes to women generally have improved throughout the world, however some prejudices remain and hiring female trainers, can be an area where such prejudice still occur.
Some animal care companies are actually reluctant to hire female trainers, believing them to be less reliable or less likely to stay, if they become pregnant. Perhaps they also consider the effect of relationships, within the training team. All of these reasons are not acceptable, neither is the thought that females could be better than male trainers. All of the reasons listed count as being forms of prejudice and should not be allowed to exist within any workplace.
Some jobs can however favour what are considered to be natural male attributes and females also, have many commonly found attributes which seem to come naturally to them. It is perhaps no coincidence that many jobs that provide care, such as nurses, nurseries, and elderly home care jobs, have a majority of female staff. Females can be seen as natural care givers, again not to prejudice against men, but it could be accepted that by nature many women understand caregiving. If we also accept that training an animal requires exceptional care, could it not be argued then that many females could perhaps start with an advantage.
I have experienced facilities that did not wish to hire females and in one case, actually fired a female trainer once she informed them she was pregnant; she was even told not to bother complaining because no-one would listen. Obviously, these attitudes are unacceptable, which rightly should be addressed through employment right law, however we all know that taking action against an employer, is costly and can damage your future employment prospects.

My advice is to be aware and prepare, when seeking a job, you could ask how many female trainers they employ, or their policy regarding maternity leave. Remember also, if a facility cares little for their employees, how should you expect they care for their animals. Do not get disheartened, rather use your natural ability and promote your caregiving tendencies to show an employer the benefits of hiring you. Animals that are cared for correctly stay healthier, live longer and are able to perform better.
Do not underestimate the power of promoting the choice of choosing a female trainer.